Invariant rotational curves in Sitnikov's Problem

The Sitnikov's Problem is a Restricted Three-Body Problem of Celestial Mechanics depending on a parameter, the eccentricity,e. The Hamiltonian,H(z, v, t, e), does not depend ont ife=0 and we have an integrable system; ife is small the KAM Theory proves the existence of invariant rotational curves, IRC. For larger eccentricities, we show that there exist two complementary sequences of intervals of values ofe that accumulate to the maximum admissible value of the eccentricity, 1, and such that, for one of the sequences IRC around a fixed point persist. Moreover, they shrink to the planez=0 ase tends to 1.     

Light curves of the eclipsing systems of RS CVn-type

This work presents the light curves for rotating spotted stars generated by a computational code developed by us. This code is based in a model of the system and its analytical solution. The work also present an analysis of the photometric curve variations with the changes in the model's parameters.As a first result we have simulated a temporal evolution of the light curve when the photospheric spot varies its size and position and we reproduced some observational light curves of the II Peg star.Work supported by Dirección de Investigación, Universidad de La Serena, Chile.     

Analysis of the spectral features of a recent supernova 1987n

We present an attempt to analyse the spectra of SN 1987n in NGC 7606, covering a period of 10 days from the time of maximum brightness. The velocities in the rest frame of NGC 7606 and the depths of the spectral lines at maximum light are very close to those of SN 1981b in NGC 4536, slight differences being nevertheless present. A distance to NGC 7606 of 46±11 Mpc for anH ₀ value of 50 km s^–1 Mpc^–1 is inferred from Pskovskii's relation.The analysis carried out within a standard simple model of spectral synthesis involves a high uncertainty in the abundance determinations for the intermediate-mass elements quoted. This uncertainty arises on the one hand from the free choice of the excitation temperature and from the sensitivity to changes in the excitation temperature of the depths of the strongest lines of those elements and, on the other hand, from the impossibility of obtaining within this model an estimate of other abundances — He, O, Na, S — which have NLTE populations.The analysis developed in a new model based (as is the standard one) on Sobolev's approximation but allowing for a more realistic continuum treatment points to an important attenuation effect on the radiation in the lines, due to the continuum scattering, which can also affect abundance determinations.     

Cosmic ray fluctuations in compressible turbulent medium

The influence of compressibility of the medium on cosmic ray (CR) fluctuations has been investigated. The CR transport equation has been used to obtain an equation for the second moment of CR particle density (correlation function of the particle density). It is shown that the effects due to the compressibility of the medium has an essential influence on CR fluctuations. The relations between CR power spectra and random velocity field have been determined. For the turbulence which is created by an ensemble of weak sound waves we have obtained the connection between the spectral indices of CR power spectra and the velocity field. It is shown that the spectral indices of CR power spectra and the velocity field of random sound waves coincide.     

Dark matter influence on velocity dispersion profiles of clusters of galaxies

We have performed a series ofN-body experiments including the effects of a massive dominant background which follows Schuster's density law in order to simulate clusters of galaxies in which a smoothly distributed dark component is present. The existence of this background is inferred from the weak luminosity segregation observed in clusters which, however, show several characteristics of well-relaxed systems. The comparison of the velocity dispersion profiles of three clusters of galaxies (Coma, Perseus, and Virgo) with those obtained in the numerical experiments allows us to place some constraints on both the distribution and amount of distributed dark material in these clusters. The profiles are rather insensitive to variations in the ratio of the background mass to the mass attached to galaxies (M _b/M_g), but exhibit a strong dependence on their relative concentration. We conclude that highly concentrated background models are not consistent with observations. We find a maximum value for the ratio of the gravitational radius of the galaxies and the background (R _g/R_b) (approximately 0.6) and using previous results (Navarroet al., 1986) we conclude that virial theorem masses underestimate the total mass (M _b+M _g) of the clusters. As a final result, we derive a minimum value for theM _b/M_g ratio. All these conclusions could apply in general if Coma, Perseus, and Virgo constitute a fair sample of the rich clusters of galaxies in the Universe.     

Runoff generation and routing on artificial slopes in a Mediterranean–continental environment: the Teruel coalfield,Spain

The aim of this study was to identify the mechanisms of runoff generation and routing and their controlling factors at the hillslope scale, on artificial slopes derived from surface coal mining reclamation in a Mediterranean–continental area. Rainfall and runoff at interrill and microcatchment scales were recorded for a year on two slopes with different substrata: topsoil cover and overburden cover. Runoff coefficient and runoff routing from interrill areas to microcatchment outlets were higher in the overburden substratum than in topsoil, and greater in the most developed rill network. Rainfall volume is the major parameter responsible for runoff response on overburden, suggesting that this substratum is very impermeable—at least during the main rainfall periods of the year (late spring and autumn) when the soil surface is sealed. In such conditions, most rainfall input is converted into runoff, regardless of its intensity. Results from artificial rainfall experiments, conducted 3 and 7 years after seeding, confirm the low infiltration capacity of overburden when sealed. The hydrological response shows great seasonal variability on the overburden slope in accordance with soil surface changes over the year. Rainfall volume and intensities (I₃₀, I₆₀) explain runoff at the interrill scale on the topsoil slope, where rainfall experiments demonstrated a typical Hortonian infiltration curve. However, no correlation was found at the microcatchment level, probably because of the loss of functionality of the only rill as ecological succession proceeded. The runoff generation mechanism on the topsoil slope is more homogeneous throughout the year. Runoff connectivity, defined as the ratio between runoff rates recorded at the rill network scale and those recorded at the interrill area scale in every rainfall event, was also greater on the rilled overburden slope, and in the most developed rill network. The dense rill networks of the overburden slope guarantee very effective runoff drainage, regardless of rainfall magnitude. Rills drain overland flow from interrill‐sealed areas, reducing the opportunity of reinfiltration in areas not affected by siltation. Runoff generation and routing on topsoil slopes are controlled by grass cover and soil moisture content, whereas on overburden slopes rill network density and soil moisture content are the main controlling factors. Copyright © 2002 John Wiley & Sons, Ltd.     

On the Centre Manifold of Collinear Points in the Planar Three-Body Problem

We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically.